# Vectors and motion in a plane [closed]

A particle travels with speed $50 m/s$ from the point $(3,-7)$ in the direction $7i-24j$ . Find its positional vector after 3 seconds.

My approach: It has travelled a distance of 150m in the direction given by the unit vector $\frac{7\hat i - 24 \hat j}{25}$ .

So, its position is now $210\hat i -720 \hat j$. But it started from $(3, - 7)$, so I have to subtract that to get $197\hat i - 713\hat j$. But I think this answer is awkward, and I may have gone wrong. So, please tell me if I am right, and if yes, can you suggest any shorter way of doing it?

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## closed as too localized by Emilio Pisanty, Qmechanic♦Jun 4 '13 at 13:13

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Displacement :$$\vec r_f-\vec r_i = \vec d =|d| \hat d$$
$\vec r_i$= position vector initial. ie. $3\hat i -7 \hat j$ ; $|d|=150m$ as found , and $\hat d$ is the direction .
$\hat d$ is just the unit vector I mentioned, right? – Saurabh Raje Jun 4 '13 at 12:00
ie$\frac{7 \hat i - 24 \hat j}{25}$ – Saurabh Raje Jun 4 '13 at 12:01
@SaurabhRaje: It's not like that . But as you sometimes do , write a new comment for every equation it's wrong. Like ""ie.eq"" must have been a part of 1st comment itself. Don't take tension though :P. – ABC Jun 4 '13 at 12:12